Step method for a functional-differential equation in Banach space

Viorica Mureșan

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Let (X, k · k) be a Banach space. Consider the following equation: x 0 (t) = K(t, x(t), x(λt), x(t − h)), t ∈ [0, b], h > 0, 0 < λ < 1, where K ∈ C([0, b] × X3 , X). By using the step method we obtain existence results for the solution of this equation.

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Mureșan, Viorica